2. '...than he' - consider the full sentence: "No one tells better jokes than he does."
3. 'Whom do you believe?" - 'whom' is the object of a sentence, whereas 'who' is the subject. Substitute a pronoun in the sentence if you are unsure - "Do you believe HIM?" is correct, not "Do you believe HE". 'You' is the subject, and the object is 'him' (or 'whom').
4. 'its effect...' - you have an effect (noun) on someone when you affect (verb) them. As for the pronoun, it refers to 'cigarette smoke', which is a singular noun.